covariance matrix

Let 𝐗=(X1,,Xn)T be a random vector. Then the covariance matrixMathworldPlanetmath of 𝐗, denoted by 𝐂𝐨𝐯(𝐗), is {Cov(Xi,Xj)}. The diagonalsMathworldPlanetmath of 𝐂𝐨𝐯(𝐗) are Cov(Xi,Xi)=Var[Xi]. In matrix notation,


It is easily seen that 𝐂𝐨𝐯(𝐗)=𝐕𝐚𝐫[𝐗] via


The covariance matrix is symmetricMathworldPlanetmathPlanetmath and if the Xi’s are independentPlanetmathPlanetmath, identically distributed (iid) with varianceMathworldPlanetmath 𝝈2, then

Title covariance matrix
Canonical name CovarianceMatrix
Date of creation 2013-03-22 14:27:23
Last modified on 2013-03-22 14:27:23
Owner CWoo (3771)
Last modified by CWoo (3771)
Numerical id 8
Author CWoo (3771)
Entry type Definition
Classification msc 62H99
Synonym variance covariance matrix